Since Sahai and Waters proposed the concept of attribute-based encryption, ciphertext-policy attribute-based encryption (CP-ABE) system has drawn more and more attentions due to its widespread use of scenes. The consumption of the battery is not economical for users who use attribute-based encryption on mobile devices because of the large number of bilinear pairing operations. Due to dynamic for user’s attributes and the openness of the access structure in the cloud environment, it may lead to the attribute failure and user privacy leakage. In order to solve above problems, we construct an attribute-based encryption scheme, which protects the privacy for the users by fully hidden access structure and supports flexible user revocation by key updating mechanisms. Meanwhile, we outsource the high computational cost of the bilinear pairing operations to the cloud storage providers, which reduces the computational expense of users for mobile devices. In order to curb cloud misconduct or malicious attacks on the cloud, we provide the verification function of the converted ciphertext which ensures the converted encrypted cipher text is not replaced illegally. The proposed scheme is more suitable for secure mobile cloud applications.